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人気のある微分積分 >

integral of (1-t)/t

解

\int \frac{1 - t}{t} d t

解

ln ∣ t ∣ - t + C

解答ステップ

\int \frac{1 - t}{t} d t

拡張

\frac{1 - t}{t} : \frac{1}{t} - 1

= \int \frac{1}{t} - 1 d t

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{t} d t - \int 1 d t

\int \frac{1}{t} d t = ln ∣ t ∣

\int 1 d t = t

= ln ∣ t ∣ - t

定数を解答に追加する

= ln ∣ t ∣ - t + C

グラフ

人気の例

y^{''}-6y^'+13y=0,y(0)=0,y^'(0)=-3

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = - 3

derivative of \sqrt[3]{sin^2(2x})

\frac{d}{d x} (3 sin^{2} (2 x))

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\int sec (1) d x

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x \to \frac{x}{4} lim (\frac{sin ( x )}{x})

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\int \frac{π}{2} \frac{π}{32} sec (2 θ) tan (2 θ) d θ